On the estimation of quasi-instantaneous frequency modulation of HF signals propagated through the ionosphere

Three methods for estimating the ionospheric frequency modulation of HF skywave signals are compared. In the first one, the instantaneous frequency is obtained by taking the time derivative of the phase of the signal, whereas, in the two other methods, autoregressive modeling using Burg and Marple algorithms is performed. High-quality signals propagated via a sporadic E-layer and backscattered by the sea surface are digitally perturbed with a known frequency modulation, and the efficiencies of the methods in recovering the perturbation is compared. The influence of the weighting of the estimator and of the number of statistical averages on the quality of the estimates is considered. It is found that, for a number of averages greater than four, the standard deviations of the difference between the estimated and the theoretical perturbation are of the same order of magnitude for the three methods, but that Marple´s algorithm yields a less biased estimate. The wave height obtained after removing the artificial modulation is recovered with an accuracy of about 10%